Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth

53 Pages Posted: 12 Dec 2017 Last revised: 23 Nov 2020

See all articles by Xue Dong He

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Zhao Li Jiang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management; National University of Singapore (NUS) - Risk Management Institute

Date Written: November 23, 2020

Abstract

In a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of her terminal wealth must exceed a target and minimizes the variance of her terminal wealth. The agent can revise her expected terminal wealth target dynamically to adapt to the change of her current wealth, and we consider the following three targets: (i) the agent's current wealth multiplied by a target expected gross return rate, (ii) the risk-free payoff of the agent's current wealth plus a premium, and (iii) a weighted average of the risk-free payoff of the agent's current wealth and a pre-set aspiration level. We derive the so-called equilibrium strategy in closed form for each of the three targets and find that the agent effectively minimizes the variance of the instantaneous change of her wealth subject to a certain constraint on the expectation of the instantaneous change of her wealth.

Keywords: portfolio selection, dynamic mean-variance analysis, time inconsistency, equilibrium policies

JEL Classification: G11, D81, C61

Suggested Citation

He, Xue Dong and Jiang, Zhao Li, Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth (November 23, 2020). Available at SSRN: https://ssrn.com/abstract=3084657 or http://dx.doi.org/10.2139/ssrn.3084657

Xue Dong He (Contact Author)

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Zhao Li Jiang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management ( email )

Hong Kong
China

National University of Singapore (NUS) - Risk Management Institute ( email )

21 Heng Mui Keng Terrace
Level 4
Singapore, 119613
Singapore

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